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Mandarinka [93]
3 years ago
12

Find the area of the shaded portion of the figure. Each vertex of square ABCD is at the center of a circle. Round your answer to

the nearest hundredth.

Mathematics
1 answer:
IrinaK [193]3 years ago
3 0

<u>Given:</u>

Each circle has a diameter of 2 inches each.

The outer square has a side length of 4 inches and the square ABCD has a side length of 2 inches.

<u>To find:</u>

The area of the shaded region.

<u>Solution:</u>

Each circle has a diameter of 2 inches. The square ABCD is at the center of each circle so it has a side length of 1 inch.

To determine the area of the shaded region, we subtract the area of the quarter-circles in the square ABCD from the area of the square ABCD.

The area of a quarter-circle =\frac{\pi r^{2} }{4} .

All the quarter-circles have a radius of 1 inch.

The area of 1 quarter-circle =\frac{\pi r^{2} }{4} = \frac{\pi (1^{2}) }{4} = \frac{3.1415}{4} .

The area of 4 quarter-circles =4(\frac{3.1415}{4}) = 3.1415.

So the area of the quarter-circles in the square ABCD is 3.1514 square inches.

The area of a square = a^{2} .

The area of square ABCD =2^{2} =4.

The area of the shaded region =4-3.1415=0.8585.

The area of the shaded region is 0.8585 square inches.

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